While "indices" is a plural of the noun index, I have never seen it used as conjugation of the verb "to index".
I see that sort of thing happen in my own typing if I'm not being careful, which I'm often not!
Here's an (inefficient) implementation in Python:
def cool_lex(s, t):
b = *t+*s
x = t
y = t
while x < s+t:
b[x-1] = 0
b[y-1] = 1
b = b[x]
b[x] = 1
x = x + 1 - (x-1)*b*(1-b)
y = b*y+1
len(set(tuple(c) for c in cool_lex(s, t))) == math.comb(s+t, s)
Edit: I tried the following, to check more correctness. It was a bad idea! Ran out of RAM with 32GB on cool_lex(14, 15).
for s in range(1, 16):
for t in range(1, 16):
if len(set(tuple(c) for c in cool_lex(s, t))) != math.comb(s+t, s):
print('bad', s, t)
I just searched for the doi with github search.
(Used “cool-lex implementation” as search string)